pith. sign in

arxiv: 2606.11788 · v1 · pith:WPSAJ7H2new · submitted 2026-06-10 · 🌌 astro-ph.HE

Centrifugal instability of compressible flows and the hydrodynamic stability of accretion disks

Serguei S. Komissarov , Konstantinos N. Gourgouliatos This is my paper

Pith reviewed 2026-06-27 09:01 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords centrifugal instabilitycompressible flowsRayleigh criterionSolberg-Høiland criterionaccretion diskshydrodynamic stabilityMach number
0
0 comments X

The pith

The centrifugal instability of compressible rotating flows depends on Mach number even in the Newtonian limit.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes a generalization of the Rayleigh criterion for centrifugal instability in pressure-supported compressible rotation. This generalization shows that instability is strongly affected by the flow Mach number, applying in both relativistic and Newtonian limits. Axisymmetric numerical simulations of non-relativistic transonic rotating flows confirm the criterion by matching predicted stability outcomes. For flows rotating about a central compact object, the derived instability criterion proves equivalent to the standard Solberg-Høiland criterion.

Core claim

A generalization of the Rayleigh criterion for compressible relativistic rotation shows the centrifugal instability depends on the flow Mach number. This holds in the Newtonian limit as well. Simulations of transonic rotating flows stable under the original Rayleigh criterion but potentially unstable under the new one agree perfectly with the theory. The criterion for accretion disks is equivalent to the Solberg-Høiland criterion, which lacks explicit Mach number dependence.

What carries the argument

The Mach-number-dependent generalization of the Rayleigh criterion for pressure-supported compressible rotation.

If this is right

  • Simulations of non-relativistic transonic flows agree perfectly with the Mach-dependent criterion.
  • The criterion applies to both relativistic and Newtonian compressible flows.
  • The derived criterion for pressure-supported rotation about a central object is equivalent to the Solberg-Høiland criterion.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Stability analyses of highly supersonic accretion disks that rely solely on the classical Rayleigh criterion may overlook Mach-number effects that the equivalent Solberg-Høiland form already incorporates.
  • The analogy between centrifugal force and gravity in the stability criteria suggests similar Mach-dependent generalizations could apply to other rotating astrophysical flows.

Load-bearing premise

The generalization of the Rayleigh criterion to compressible pressure-supported rotation is taken as given from prior analysis.

What would settle it

An axisymmetric simulation of a transonic Newtonian rotating flow that is stable according to the classical Rayleigh criterion but shows instability (or vice versa) according to the Mach-dependent criterion.

Figures

Figures reproduced from arXiv: 2606.11788 by Konstantinos N. Gourgouliatos, Serguei S. Komissarov.

Figure 1
Figure 1. Figure 1: Stable and unstable domains in the models with p0 = 0.1 (top panel) and in the models with p0 = 1.0 (bottom panel). In the unstable domains, d ln Ψ/d ln R − M2 < 0. These structures are reminiscent of numerical fluid jets stud￾ied in connection to the jets of active galactic nuclei. The jets may extend well beyond the instability domain and cre￾ate an extended zone of turbulent flow. For example, the insta… view at source ↗
Figure 2
Figure 2. Figure 2: The density distribution at t = 10, 15, 50 for the model CYL-C (top panels), CYL-D (middle panels) and CYL-F (bottom panels). For instability, the force derivative has to be positive, and hence the instability criterion reads ρv2 ϕ R2 d ln Ψ d ln R − M2 R dp dR + GM R2 ρ γ dS dR < 0 . (23) To understand the physical nature of the instability, it is instructive to consider the limits of vanishing gravity an… view at source ↗
read the original abstract

A recent analysis of the centrifugal instability in the case of pressure-supported compressible relativistic rotation, with application to astrophysical jets, yielded a generalisation of the famous Rayleigh criterion for Newtonian flows. According to this criterion, the centrifugal instability is strongly affected by the flow Mach number, and not only in the relativistic fluid dynamics but also in its Newtonian limit. To validate the Newtonian version of this criterion, we performed axisymmetric numerical simulations of non-relativistic transonic rotating flows which are stable according to the original Rayleigh criterion but can be either stable or unstable according to the new one. The results of computer simulations are found to be in perfect agreement with the theory. The hydrodynamic stability of accretion disks is often explained by referring to the original Rayleigh criterion, even if their rotation is highly supersonic. To clarify the matter, we analysed the hydrodynamic stability of flows rotating about central compact object and derived an instability criterion that retains the explicit dependence on the flow Mach number. This criterion turns out to be equivalent to the standard Solberg-H{\o}iland criterion, which does not involve the Mach number. The same applies to the case of pressure-supported rotation, where the role of gravity is played by the centrifugal force.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper generalizes the Rayleigh criterion for centrifugal instability to compressible pressure-supported rotation, showing Mach number dependence even in the Newtonian limit. It validates the Newtonian transonic case via axisymmetric simulations of flows stable by the original Rayleigh criterion but potentially unstable by the new criterion, reporting perfect agreement with theory. For accretion disks, it derives a Mach-dependent instability criterion shown to be equivalent to the standard Solberg-Høiland criterion.

Significance. If the results hold, the work supplies targeted numerical validation for the compressible generalization in the Newtonian regime and resolves applicability questions for supersonic accretion disks by establishing mathematical equivalence to the Solberg-Høiland criterion. The simulation agreement and the equivalence demonstration are explicit strengths that support the central claims without introducing free parameters.

major comments (1)
  1. The validation of the Newtonian transonic case rests on the claim that simulation results are in 'perfect agreement' with the generalized criterion. The manuscript should report quantitative measures of this agreement (e.g., comparison of measured growth rates to theoretical predictions) and details on simulation parameters such as resolution, initial perturbation amplitudes, and case selection criteria to substantiate the load-bearing validation result.
minor comments (2)
  1. The abstract states that the disk criterion 'turns out to be equivalent' to Solberg-Høiland; the main text should include an explicit cross-reference to the equations or subsection where the algebraic equivalence is demonstrated.
  2. Clarify in the introduction or methods the precise scope of the new contribution versus the referenced prior compressible generalization to avoid any ambiguity about what is being validated here.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and the recommendation of minor revision. The single major comment concerns the presentation of the numerical validation, which we address below.

read point-by-point responses

  1. Referee: The validation of the Newtonian transonic case rests on the claim that simulation results are in 'perfect agreement' with the generalized criterion. The manuscript should report quantitative measures of this agreement (e.g., comparison of measured growth rates to theoretical predictions) and details on simulation parameters such as resolution, initial perturbation amplitudes, and case selection criteria to substantiate the load-bearing validation result.

    Authors: We agree that the current description of the simulation results would benefit from quantitative support. In the revised manuscript we will add a direct comparison of the growth rates extracted from the simulations against the analytic predictions of the generalized criterion, together with the requested technical details on resolution, initial perturbation amplitudes, and case selection. These additions will be placed in the section describing the Newtonian validation runs. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation chain is self-contained

full rationale

The paper imports the compressible generalization of the Rayleigh criterion from a cited prior analysis but does not claim to re-derive it here; instead it validates the Newtonian transonic case via independent axisymmetric simulations of flows stable under the original Rayleigh criterion. The accretion-disk criterion is derived directly in the present work and shown mathematically equivalent to the Solberg-Høiland criterion through the paper's own analysis, without any reduction of predictions to fitted parameters, self-definitional loops, or load-bearing self-citations that lack external verification. No step equates an output to its input by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract only; no explicit free parameters, axioms, or invented entities are stated. The work relies on standard assumptions of ideal fluid dynamics and axisymmetric perturbations.

pith-pipeline@v0.9.1-grok · 5749 in / 1144 out tokens · 16945 ms · 2026-06-27T09:01:14.127753+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

49 extracted references · 33 canonical work pages · 6 internal anchors

  1. [1]

    Proceedings of the Royal Society of London Series A , year = 1917, month = mar, volume =

    On the Dynamics of Revolving Fluids. Proceedings of the Royal Society of London Series A , year = 1917, month = mar, volume =. doi:10.1098/rspa.1917.0010 , adsurl =

    work page doi:10.1098/rspa.1917.0010 1917

  2. [2]

    Transient dynamics of rotating shear flow

    Accretion disk instability revisited. Transient dynamics of rotating shear flow. , keywords =. doi:10.1051/0004-6361:20041273 , adsurl =

    work page doi:10.1051/0004-6361:20041273

  3. [3]

    Reconfinement and Loss of Stability in Jets from Active Galactic Nuclei

    Reconfinement and loss of stability in jets from active galactic nuclei. Nature Astronomy , keywords =. doi:10.1038/s41550-017-0338-3 , archivePrefix =. 1806.05683 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1038/s41550-017-0338-3

  4. [4]

    , keywords =

    The stability of nonuniform rotation in relativistic stars. , keywords =. doi:10.1086/153563 , adsurl =

    work page doi:10.1086/153563

  5. [5]

    , keywords =

    Centrifugal instability of the jovian magnetosphere and its interaction with the solar wind. , keywords =. doi:10.1016/0032-0633(74)90015-4 , adsurl =

    work page doi:10.1016/0032-0633(74)90015-4

  6. [6]

    Journal of Physical Oceanography , year = 2015, month = jun, volume =

    The Energetics of Centrifugal Instability. Journal of Physical Oceanography , year = 2015, month = jun, volume =. doi:10.1175/JPO-D-14-0064.1 , adsurl =

    work page doi:10.1175/jpo-d-14-0064.1 2015

  7. [7]

    EGU General Assembly Conference Abstracts , year = 2020, series =

    Centrifugal Instability of a Geostrophic Jet. EGU General Assembly Conference Abstracts , year = 2020, series =. doi:10.5194/egusphere-egu2020-3610 , adsurl =

    work page doi:10.5194/egusphere-egu2020-3610 2020

  8. [8]

    NASA STI/Recon Technical Report A , keywords =

    Hydrodynamic stability. NASA STI/Recon Technical Report A , keywords =

  9. [9]

    Annual Review of Fluid Mechanics , keywords =

    Instability mechanisms in shear-flow transition. Annual Review of Fluid Mechanics , keywords =. doi:10.1146/annurev.fl.20.010188.002043 , adsurl =

    work page doi:10.1146/annurev.fl.20.010188.002043

  10. [10]

    , keywords =

    Role of Compressibility, Turbulent Viscosity, and Mass-Transfer-Rate on Accretion Discs in Close Binaries. , keywords =. doi:10.1093/pasj/60.2.259 , adsurl =

    work page doi:10.1093/pasj/60.2.259

  11. [11]

    Solar System Research , year = 2024, month = mar, volume =

    On the Modeling of a Compressible MHD Turbulence of an Accretion Protoplanetary Disk. Solar System Research , year = 2024, month = mar, volume =. doi:10.1134/S0038094623070067 , adsurl =

    work page doi:10.1134/s0038094623070067 2024

  12. [12]

    The reconfinement of AGN jets

    The reconfinement of AGN jets. arXiv e-prints , keywords =. doi:10.48550/arXiv.1811.06764 , archivePrefix =. 1811.06764 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1811.06764

  13. [13]

    , keywords =

    A structure and energy dissipation efficiency of relativistic reconfinement shocks. , keywords =. doi:10.1111/j.1365-2966.2008.14123.x , archivePrefix =. 0810.3912 , primaryClass =

    work page doi:10.1111/j.1365-2966.2008.14123.x 2008

  14. [14]

    , keywords =

    Numerical simulations of jets. , keywords =. doi:10.1016/j.newar.2021.101610 , adsurl =

    work page doi:10.1016/j.newar.2021.101610 2021

  15. [15]

    Relativistic Centrifugal Instability

    Relativistic centrifugal instability. , keywords =. doi:10.1093/mnrasl/sly016 , archivePrefix =. 1710.01345 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnrasl/sly016

  16. [16]

    , keywords =

    How do recollimation-induced instabilities shape the propagation of hydrodynamic relativistic jets?. , keywords =. doi:10.1051/0004-6361/202554698 , archivePrefix =. 2503.18602 , primaryClass =

    work page doi:10.1051/0004-6361/202554698

  17. [17]

    , keywords =

    The structure of hydrodynamic -ray burst jets. , keywords =. doi:10.1093/mnras/staa3501 , archivePrefix =. 2006.02466 , primaryClass =

    work page doi:10.1093/mnras/staa3501 2006

  18. [18]

    2024 , eprint=

    Gauging Centrifugal Instabilities in Compressible Free-Shear Layers Via Nonlinear Boundary Region Equations , author=. 2024 , eprint=

    2024

  19. [19]

    Z. Angew. Math. Mech. , year = 1955, volume =

    1955

  20. [20]

    Greene , year=

    Fei Li and Meelan Choudhari and Chau-Lyan Chang and Minwei Wu and Patrick T. Greene , year=. Development and Breakdown of Goertler Vortices in High Speed Boundary Layers , booktitle =

  21. [21]

    Journal of Fluid Mechanics , year=

    On the spatial evolution of centrifugal instabilities within curved incompressible mixing layers , author=. Journal of Fluid Mechanics , year=

  22. [22]

    Boiko and Andrey V

    Andrey V. Boiko and Andrey V. Ivanov and Y. S. Kachanov and D. A. Mischenko , journal=. Steady and unsteady G. 2010 , volume=

    2010

  23. [23]

    Bayly, B. J. , title =. The Physics of Fluids , volume =. 1988 , month =. doi:10.1063/1.867002 , url =

    work page doi:10.1063/1.867002 1988

  24. [24]

    Nat Commun , year=

    Topographic generation of submesoscale centrifugal instability and energy dissipation , author=. Nat Commun , year=

  25. [25]

    Global Climatology of Tropospheric Inertial Instability , author=. J. Atmos. Sci. , year=

  26. [26]

    , year = 1967, month = nov, volume =

    Differential Rotation in Stars. , year = 1967, month = nov, volume =. doi:10.1086/149360 , adsurl =

    work page doi:10.1086/149360 1967

  27. [27]

    a t station \

    Instabilit \"a t station \"a rer Rotation in Sternen. , year = 1968, month = jan, volume =

    1968

  28. [28]

    Annual Review of Fluid Mechanics , year = 1994, volume = 26, pages =

    Gurtler vortices. Annual Review of Fluid Mechanics , year = 1994, volume = 26, pages =. doi:10.1146/annurev.fl.26.010194.002115 , adsurl =

    work page doi:10.1146/annurev.fl.26.010194.002115 1994

  29. [29]

    MPI-AMRVAC for Solar and Astrophysics

    doi:10.1088/0067-0049/214/1/4 , Eid =. arXiv , Author =:1407.2052 , Journal =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0067-0049/214/1/4 2052

  30. [30]

    Keppens and Z

    R. Keppens and Z. Meliani and A.J. van Marle and P. Delmont and A. Vlasis and B. van der Holst , Date-Added =. Parallel, grid-adaptive approaches for relativistic hydro and magnetohydrodynamics , Url =. Journal of Computational Physics , Keywords =. doi:https://doi.org/10.1016/j.jcp.2011.01.020 , Issn =

    work page doi:10.1016/j.jcp.2011.01.020 2011

  31. [31]

    , keywords =

    Self-similar jets. , keywords =

  32. [32]

    , archivePrefix = "arXiv", eprint =

    Causality and stability of cosmic jets. , archivePrefix = "arXiv", eprint =. doi:10.1093/mnras/stv1295 , adsurl =

    work page doi:10.1093/mnras/stv1295

  33. [33]

    Observational appearance

    Black holes in binary systems. Observational appearance. , year = 1973, month = jan, volume =

    1973

  34. [34]

    I - Linear analysis

    A powerful local shear instability in weakly magnetized disks. I - Linear analysis. II - Nonlinear evolution. , keywords =. doi:10.1086/170270 , adsurl =

    work page doi:10.1086/170270

  35. [35]

    , keywords =

    Enhanced Angular Momentum Transport in Accretion Disks. , keywords =. 2003. doi:10.1146/annurev.astro.41.081401.155207 , archivePrefix =. astro-ph/0306208 , primaryClass =

    work page doi:10.1146/annurev.astro.41.081401.155207 2003

  36. [36]

    Proceedings of the National Academy of Science , year = 1960, month = feb, volume =

    The Stability of Non-Dissipative Couette Flow in Hydromagnetics. Proceedings of the National Academy of Science , year = 1960, month = feb, volume =. doi:10.1073/pnas.46.2.253 , adsurl =

    work page doi:10.1073/pnas.46.2.253 1960

  37. [37]

    , keywords =

    Nonlinear Stability, Hydrodynamical Turbulence, and Transport in Disks. , keywords =. doi:10.1086/177585 , adsurl =

    work page doi:10.1086/177585

  38. [38]

    Stability

    The Hydrodynamics of Accretion Discs I. Stability. , year = 1975, month = aug, volume =

    1975

  39. [39]

    Hydrodynamic stability in accretion disks under the combined influence of shear and density stratification

    Hydrodynamic stability in accretion disks under the combined influence of shear and density stratification. , keywords =. doi:10.1051/0004-6361:20020853 , archivePrefix =. astro-ph/0202246 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361:20020853

  40. [40]

    U ber die freien Schwingungen einer homogenen Fl \

    \"U ber die freien Schwingungen einer homogenen Fl \"u ssigkeitsschicht auf der rotierenden Erde. I. Mit 4 Textfiguren. Astrophysica Norvegica , year = 1936, month = jan, volume =

    1936

  41. [41]

    PhD thesis , booktitle =

    H. PhD thesis , booktitle =. 1941 , volume =

    1941

  42. [42]

    Accretion Power in Astrophysics: Third Edition

  43. [43]

    Foundations of Black Hole Accretion Disk Theory

    Foundations of Black Hole Accretion Disk Theory. Living Reviews in Relativity , keywords =. doi:10.12942/lrr-2013-1 , archivePrefix =. 1104.5499 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.12942/lrr-2013-1 2013

  44. [44]

    Chandrasekhar, S , title =

  45. [45]

    1987 , isbn =

    Fluid Mechanics , publisher =. 1987 , isbn =. doi:https://doi.org/10.1016/B978-0-08-033933-7.50009-X , url =

    work page doi:10.1016/b978-0-08-033933-7.50009-x 1987

  46. [46]

    Geophysical and Astrophysical Fluid Dynamics , keywords =

    The convective stability of a thin viscous disc. Geophysical and Astrophysical Fluid Dynamics , keywords =. doi:10.1080/03091929308203593 , adsurl =

    work page doi:10.1080/03091929308203593

  47. [47]

    Axisymmetric Perturbations of Thin Gaseous Disks. I. Unstable Convective Modes and Their Consequences for the Solar Nebula. , keywords =. doi:10.1086/166418 , adsurl =

    work page doi:10.1086/166418

  48. [48]

    , keywords =

    Magnetic and vertical shear instabilities in accretion discs. , keywords =. doi:10.1046/j.1365-8711.1998.01118.x10.1111/j.1365-8711.1998.01118.x , adsurl =

    work page doi:10.1046/j.1365-8711.1998.01118.x10.1111/j.1365-8711.1998.01118.x 1998

  49. [49]

    , keywords =

    Simulations of vertical shear instability in accretion discs. , keywords =. doi:10.1051/0004-6361:20035896 , adsurl =

    work page doi:10.1051/0004-6361:20035896